65ed4

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 63ed4 65ed4 67ed4 →
Prime factorization 5 × 13
Step size 36.9231¢ 
Octave 33\65ed4 (1218.46¢)
Twelfth 52\65ed4 (1920¢) (→4\5ed4)
Consistency limit 1
Distinct consistency limit 1

65 equal divisions of the 4th harmonic (abbreviated 65ed4) is a nonoctave tuning system that divides the interval of 4/1 into 65 equal parts of about 36.9 ¢ each. Each step represents a frequency ratio of 41/65, or the 65th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 36.9
2 73.8 23/22
3 110.8 33/31
4 147.7
5 184.6
6 221.5 33/29
7 258.5
8 295.4
9 332.3 17/14, 23/19
10 369.2 21/17, 26/21
11 406.2 19/15
12 443.1 22/17
13 480 29/22
14 516.9 31/23
15 553.8
16 590.8 31/22
17 627.7 33/23
18 664.6 22/15
19 701.5 3/2
20 738.5 23/15, 26/17
21 775.4
22 812.3
23 849.2 31/19
24 886.2
25 923.1 29/17
26 960
27 996.9
28 1033.8
29 1070.8 13/7
30 1107.7 19/10
31 1144.6 29/15, 33/17
32 1181.5
33 1218.5
34 1255.4 31/15
35 1292.3
36 1329.2
37 1366.2 11/5
38 1403.1 9/4
39 1440 23/10
40 1476.9
41 1513.8
42 1550.8
43 1587.7
44 1624.6
45 1661.5
46 1698.5
47 1735.4
48 1772.3
49 1809.2
50 1846.2 29/10
51 1883.1
52 1920
53 1956.9 31/10
54 1993.8
55 2030.8
56 2067.7 33/10
57 2104.6 27/8
58 2141.5
59 2178.5
60 2215.4
61 2252.3
62 2289.2
63 2326.2
64 2363.1
65 2400

Harmonics

Approximation of harmonics in 65ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +18.5 +18.0 +0.0 -17.1 -0.4 -8.8 +18.5 -0.8 +1.4 -15.9 +18.0
Relative (%) +50.0 +48.9 +0.0 -46.3 -1.1 -23.9 +50.0 -2.3 +3.7 -43.2 +48.9
Steps
(reduced)
33
(33)
52
(52)
65
(0)
75
(10)
84
(19)
91
(26)
98
(33)
103
(38)
108
(43)
112
(47)
117
(52)
Approximation of harmonics in 65ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -9.8 +9.6 +1.0 +0.0 +5.8 +17.6 -2.1 -17.1 +9.2 +2.5 -0.6
Relative (%) -26.4 +26.1 +2.6 +0.0 +15.7 +47.7 -5.8 -46.3 +25.0 +6.8 -1.6
Steps
(reduced)
120
(55)
124
(59)
127
(62)
130
(0)
133
(3)
136
(6)
138
(8)
140
(10)
143
(13)
145
(15)
147
(17)